Full thermoelectric characterization of a single molecule

Molecules are predicted to be chemically tunable towards high thermoelectric efficiencies and they could outperform existing materials in the field of energy conversion. However, their capabilities at the more technologically relevant temperature of 300 K are yet to be demonstrated. A possible reason could be the lack of a comprehensive technique able to measure the thermal and (thermo)electrical properties, including the role of phonon conduction. Here, by combining the break junction technique with a suspended heat-flux sensor, we measured the total thermal and electrical conductance of a single molecule, at room temperature, together with its Seebeck coefficient. We used this method to extract the figure of merit zT of a tailor-made oligo(phenyleneethynylene)-9,10-anthracenyl molecule with dihydrobenzo[b]thiophene anchoring groups (DHBT-OPE3-An), bridged between gold electrodes. The result is in excellent agreement with predictions from density functional theory and molecular dynamics. This work represents the first measurement, within the same setup, of experimental zT of a single molecule at room temperature and opens new opportunities for the screening of several possible molecules in the light of future thermoelectric applications. The protocol is verified using SAc-OPE3, for which individual measurements for its transport properties exist in the literature.


Meaning of zT and Efficiency
By combining the three measured quantity as described in eq.1 in the main text it is possible to determine experimentally the figure-of-merit zT.
The figure of merit indicates how close a system is to the theoretical maximum efficiency, i.e. a Carnot machine working between the same temperature difference. The optimum condition for maximum efficiency is indeed: where and are the hot-and cold-side temperatures, respectively. The thermoelectric conversion efficiency is the product of the Carnot efficiency ( − / ) and a reduction factor as a function of the material's figure of merit zT, taken at = + 2 , where = − as difference of fits and thermal background slope A plateau of constant thermal conductance is usually not observed in the thermal signal 7,8 . Instead, a linear decrease versus tip displacement is usually present, with slopes ranging between 0.5 and 2 nW/(K nm). This is caused by spurious thermal conductance paths around the actual molecular junction, that forms a thermal background, which is modulated by tip retraction. As already pointed out by Mosso et al. 7 , those paths can be attributed essentially to three effects. The first effect is the thermal near-field radiation occurring between the tip and the platform even for nominally clean surfaces 9,10 . The second is due to the presence of possible solvent residues which, despite the cleaning procedure, can still be present on the surface. The third contribution comes from the deposited molecules themselves, that are not directly bound to the electrodes but can anyway establish a thermal contact through Van der Waals bonds 11,12,13 . A plateau of constant thermal conductance is usually not observed in the thermal signal. Indeed, a linear decrease versus tip displacement is usually present, with slopes ranging between 0.5 and 2 nW/(K nm). This is caused by spurious thermal conductance paths around the actual molecular junction, that forms a thermal background, which is modulated by tip retraction. As already discussed in details in Mosso et al. 7 , those paths can be attributed to three effects. First, even nominally clean gold surfaces can show significant heat transfer of this magnitude due to thermal near-field radiation 9,10 . The magnitude of this contribution is currently under debate 9,10 . It is worth to mention that, recently, thermal conductance variations vs. tip−surface distance have been reported in near-field measurements in UHV, even after thorough in situ cleaning procedures. Those measurements exhibit background slopes between 0.5 and 8 nW/K/nm, close to the range reported in this study 9,10 . Those measurements suggest that contributions due to radiative processes at nm distances might not be ignored, and most likely might not be avoided experimentally. Second, despite the cleaning processes, there still might be residues and/or contaminants on the surface coming from the MEMS fabrication steps and exposure to the solvent. Third, also the deposited molecules that are not directly bound to the electrodes can establish a thermal contact. All those adsorbates appear electrically inactive, because only weakly bonded to the electrodes, but able to carry significant heat, on the order of 10−30 nW/K, via Van der Waals bonds 11,12,13 . Due to the differential scheme for measuring the thermal conductance, the reproducibility and the slope of the thermal background signal are more important than its magnitude. Within our experimental conditions, the thermal background results stable and does not vary significantly during repeated cycles of the breakjunction event, remaining approximately linear in the region of few ångströms around the breaking point of the molecular plateau. On a larger length scale, however, there is no prior assumption on the linearity of the background signal.

Phononic heat flux spectrum
To further analyze the vibrational modes involved in phonon thermal transport across the molecule, we have also computed the phonon spectral thermal conductance using MD simulations 14,15 . Figure  4 compares the thermal conductance of DHBT-OPE3-An and DHBT-OPE3 molecule junctions. Note that due to the low Debye frequency of gold (~260 cm -1 ) 16 phonons with energies higher than 260 cm -1 are filtered out and not included in the histogram. Below that frequency, the two spectra match relatively well except at low frequencies ( Figure S1). The relative discrepancies observed are related to the effect of the pending groups which should act here as a low frequency filter.

Rigidity of the molecule
To confirm the rigidity of the backbone of the OPE3 derivative, the torsion of the molecule junctions has been studied by means of MD simulations. The torsion angles between phenylene groups in the course of a 20 ns trajectory did not exceed 10 degrees and the DHBT-OPE-An remained planar 17 . Our studies show that the metal-molecule interface has a high conformational rigidity due to the DHBT anchor group 14 .

Reference measurement using SAc-OPE3
In order to verify the protocol to measure the Seebeck coefficient, it was also applied to the same molecule that was previously examined in the same setup, namely the OPE3 molecule with standard thioacetate end groups (SAc-OPE3), for which the thermal conductivity was reported by Mosso et al. 7 in agreement with observations by Cui et al. 8 . The protocol to measure Seebeck coefficient was applied also to this molecule yielding 7.9 ± 4 V/K. This is in agreement with literature values obtained for single molecules and self-assembled monolayers, namely 8.0 ± 0.8 V/K 17 , 7.78 ± 0.34 V/K 18 , and 9.7 ± 0.2 V/K 19 .
This makes SAc-OPE3 the second molecule for which the entire zT was measured using this protocol, yielding zT ≃ 2x10 -5 .